Date: Fri, 19 Jul 1996 16:11:20 -0400 (EDT)
Subject: Re: Russell Paradox
Nicolas,
If you're talking about the same Russell paradox that I know,
one of my professors gave an excellent example of the paradox.
Here it is...
Think about a set A, with an interesting definition: A is the
set of all the things that aren't in A , i.e.,
A = {x : x not in A}
Now, consider some element, e. Is e in A or not in A?
Let's say e is in A. Then by the definition of A, we must
conclude it is not in A, since A is only made up of elements
that aren't in it. So it can't be in A. But if e isn't in A,
then by definition, e is in A. So e can't not be in A.
That's the paradox, at least how it was introduced to me.
I know it may be tough to follow this, it is a much easier
thing to explain in person, but I hope this helps.
You can find a slightly different formulation of the paradox,
along with Russell's recollection of how he came up with it at
http://www.cut-the-knot.org/selfreference/russell.shtml
If you have any other questions or want any clarification,
feel free to write again!
-Doctor Erich, The Math Forum
Check out our web site! http://mathforum.org/dr.math/